Formation and order of matrix

Chapter 3 Class 12 Matrices
Concept wise

Letβs consider the matrix

It has 2 rows & 2 columns

So, we write the order as

And,

Β  3, 2, 1, 4 are elements of matrix A

Β

We write the matrix A as

Where

a 11 β element in 1st row, 1st column

a 12 β element in 1st row, 2nd column

a 21 β element in 2nd row, 1st column

a 22 β element in 2nd row, 2nd column

Β

So,

Β  Β  a 11 = 3

Β  Β  a 12 = 2

Β  Β  a 21 = 1

Β  Β  a 22 = 4

Β

For matrix

Β

It has 3 rows & 2 columns

So, the order is 3 Γ 2.

Β

We write matrix B as

Β

Similarly,

Β

## a ij = i + j

Β

A 4 Γ 3 matrix looks like

Now,

a 11 = 1 + 1 = 2

a 12 = 1 + 2 = 3

a 13 = 1 + 3 = 4

a 21 = 2 + 1 = 3

a 22 = 2 + 2 = 4

a 23 = 2 + 3 = 5

a 32 = 3 + 2 = 5

a 33 = 3 + 3 = 6

a 41 = 4 + 1 = 5

a 42 = 4 + 2 = 5

a 43 = 4 + 3 = 7

Β

So, our matrix is

Β

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### Transcript

A = [β 8(3&[email protected]&4)] 2 Γ 2 Rows Column And, 3, 2, 1, 4 are elements of matrix A A = [β 8(π_11&π[email protected]π_21&π_22 )] B = [β 8(3&[email protected]&[email protected]&3)] B = [β 8(3&[email protected]&[email protected]&3)]_(3 Γ 2) Matrix Order [β 8(9&5&[email protected]&8&[email protected]&1&6)] 3 Γ 3 [β 8(1&2&5&8&π₯&π§)] 1 Γ 6 [β 8([email protected]@[email protected]π¦@tan^(β1)β‘π₯ )] 5 Γ 1 [β 8(sinβ‘π₯&cosβ‘π₯&tanβ‘π₯&cotβ‘π₯@sinβ‘π¦&cosβ‘π¦&tanβ‘π¦&cotβ‘π¦@sinβ‘π§&cosβ‘π§&tanβ‘π§&cotβ‘π§ )] 3 Γ 4 A = [β 8(π_11&π_12&π[email protected]π_21&π_22&π[email protected]π_31&π_32&π[email protected]π_41&π_42&π_43 )] A = [β 8(2&3&[email protected]&4&[email protected]&5&[email protected]&6&7)] A = [β 8(2&3&[email protected]&4&[email protected]&5&[email protected]&6&7)]

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.